The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the o...The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.展开更多
We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-d...We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11847245,11874393,and 12134015)the Doctoral Scientific Research Foundation of Yunnan Normal University(Grant No.00900205020503180)+2 种基金the National Natural Science Foundation of China(Grant Nos.12275214,11805152,12047502,and 11947301)the Natural Science Basic Research Program of Shaanxi Province(Grant Nos.2021JCW-19and 2019JQ-107)the Shaanxi Key Laboratory for Theoretical Physics Frontiers in China。
文摘The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.
基金the National Natural Science Foundation of China(Grant Nos.11847245 and 11874393).
文摘We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.
